Subgroups — C₂×C₃²×#949 #13179200

Order 1728.

2444 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃³×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃²×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×#949	C₂	1	8	yes	maximal, direct product factor
4	C₂×C₃²×#215	C₂	1	2	yes	maximal, complemented
5	C₂×C₃²×#213	C₂	1	2	yes	maximal, complemented
6	C₂×C₃²×#208	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃²×AGL(1,ℤ/8)	—	3	1	no	maximal
8	C₂×C₃×#949	C₃	1	4	yes	maximal, direct product factor
9	C₂³×C₃²×D₃	—	2	1	no	—
10	C₃³×#41	—	2	2	no	—
11	C₃³×#41	C₂²	1	4	yes	complemented
12	C₂×C₃³×Q₈	C₂²	1	1	yes	characteristic, complemented
13	C₂×C₃³×D₄	—	2	1	no	—
14	C₂×C₃³×D₄	C₂²	1	1	yes	characteristic, complemented
15	C₂²×C₃³×C₄	—	2	1	no	—
16	C₂²×C₃³×C₄	C₂²	1	1	yes	characteristic
17	C₂×C₃²×D₁₂	—	2	2	no	—
18	C₂×C₃²×D₁₂	—	2	1	no	—
19	C₂×C₃²×D₁₂	C₂²	1	2	yes	—
20	C₂×C₃²×D₁₂	C₂²	1	4	yes	complemented
21	C₃²×#215	C₂²	1	8	yes	complemented
22	C₃²×#213	C₂²	1	8	yes	complemented
23	C₃²×#208	C₂²	1	4	yes	complemented
24	C₂×C₃²×C₃⋊C₈	C₂²	1	2	yes	complemented
25	C₂×C₃²×#41	—	2	4	no	—
26	C₂×C₃²×#41	D₃	1	1	yes	characteristic, complemented
27	C₂×C₃²×#41	C₂×C₃	1	4	yes	complemented
28	C₂²×C₃²×D₄	—	3	1	no	—
29	C₂²×C₃×D₁₂	C₂×C₃	1	4	yes	complemented
30	C₃²×AGL(1,ℤ/8)	—	3	8	no	—
31	C₂×C₃²×SD₁₆	—	3	2	no	—
32	C₂×C₃²×D₈	—	3	2	no	—
33	C₂×C₃²×M₁₆	—	3	1	no	—
34	C₃×#949	C₂×C₃	1	32	yes	direct product factor
35	C₂×C₃×#215	C₂×C₃	1	8	yes	complemented
36	C₂×C₃×#213	C₂×C₃	1	8	yes	complemented
37	C₂×C₃×#208	C₂×C₃	1	4	yes	complemented
38	C₂³×C₃³	—	2	1	no	—
39	C₂³×C₃³	D₄	1	1	yes	characteristic
40	C₂²×C₃²×D₃	—	2	2	no	—
41	C₂²×C₃²×D₃	—	2	4	no	—
42	C₂²×C₃²×D₃	—	4	4	no	—
43	C₃³×Q₈	—	2	1	no	—
44	C₃³×Q₈	C₂³	1	2	yes	complemented
45	C₃³×D₄	—	2	4	no	—
46	C₃³×D₄	—	2	1	no	—
47	C₃³×D₄	C₂³	1	2	yes	complemented
48	C₂×C₃³×C₄	—	2	1	no	—
49	C₂×C₃³×C₄	—	2	4	no	—
50	C₂×C₃³×C₄	D₄	1	1	yes	characteristic
51	C₂×C₃³×C₄	D₄	1	2	yes	—
52	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
53	C₂×C₃³×C₄	C₂³	1	2	yes	—
54	C₃²×D₁₂	—	2	2	no	—
55	C₃²×D₁₂	—	2	4	no	—
56	C₃²×D₁₂	C₂³	1	4	yes	—
57	C₃²×C₃⋊C₈	C₂³	1	4	yes	complemented
58	C₂×C₃×AGL(1,ℤ/8)	—	3	4	no	—
59	C₂×#949	C₃²	1	1	yes	characteristic, direct product factor
60	C₂⁴×C₃²	—	6	1	no	—
61	C₂³×C₃×D₃	—	2	4	no	—
62	C₃²×#41	—	2	16	no	—
63	C₃²×#41	—	2	16	no	—
64	C₃²×#41	—	2	2	no	—
65	C₃²×#41	—	2	8	no	—
66	C₃²×#41	C₂×D₃	1	4	yes	complemented
67	C₃²×#41	C₂²×C₃	1	16	yes	complemented
68	C₂×C₃²×Q₈	—	2	4	no	—
69	C₂×C₃²×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
70	C₂×C₃²×Q₈	C₂²×C₃	1	4	yes	complemented
71	C₂×C₃²×D₄	—	2	8	no	—
72	C₂×C₃²×D₄	—	2	4	no	—
73	C₂×C₃²×D₄	—	2	1	no	—
74	C₂×C₃²×D₄	—	2	4	no	—
75	C₂×C₃²×D₄	—	3	2	no	—
76	C₂×C₃²×D₄	—	3	4	no	—
77	C₂×C₃²×D₄	—	6	2	no	—
78	C₂×C₃²×D₄	—	6	1	no	—
79	C₂×C₃²×D₄	C₂×D₃	1	1	yes	characteristic, complemented
80	C₂×C₃²×D₄	C₂²×C₃	1	4	yes	complemented
81	C₂²×C₃²×C₄	—	2	8	no	—
82	C₂²×C₃²×C₄	—	2	4	no	—
83	C₂²×C₃²×C₄	—	2	1	no	—
84	C₂²×C₃²×C₄	—	2	4	no	—
85	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic
86	C₂²×C₃²×C₄	C₂²×C₃	1	4	yes	—
87	C₂×C₃×D₁₂	—	2	8	no	—
88	C₂×C₃×D₁₂	—	2	4	no	—
89	C₂×C₃×D₁₂	C₂²×C₃	1	8	yes	—
90	C₂×C₃×D₁₂	C₂²×C₃	1	16	yes	complemented
91	C₃²×SD₁₆	—	3	8	no	—
92	C₃²×D₈	—	3	8	no	—
93	C₃²×M₁₆	—	3	4	no	—
94	C₂×C₃²×C₈	—	3	2	no	—
95	C₃×#215	C₂²×C₃	1	32	yes	complemented
96	C₃×#213	C₂²×C₃	1	32	yes	complemented
97	C₃×#208	C₂²×C₃	1	16	yes	complemented
98	C₂×C₃×C₃⋊C₈	C₂²×C₃	1	8	yes	complemented
99	C₂²×C₃³	—	2	2	no	—
100	C₂²×C₃³	—	2	2	no	—
101	C₂²×C₃³	—	4	2	no	—
102	C₂²×C₃³	C₂×D₄	1	2	yes	—
103	C₂²×C₃³	C₂×D₄	1	1	yes	characteristic
104	C₂×C₃²×D₃	—	2	4	no	—
105	C₂×C₃²×D₃	—	4	8	no	—
106	C₂×C₃²×D₃	—	4	4	no	—
107	C₃³×C₄	—	2	2	no	—
108	C₃³×C₄	C₂×D₄	1	2	yes	—
109	C₃³×C₄	C₂×D₄	1	1	yes	characteristic
110	C₃³×C₄	C₂⁴	1	1	yes	characteristic
111	C₂×C₃×#41	—	2	4	no	—
112	C₂×C₃×#41	C₃×D₃	1	4	yes	complemented
113	C₂×C₃×#41	C₂×C₃²	1	1	yes	characteristic, complemented
114	C₂²×C₃×D₄	—	3	4	no	—
115	C₂²×D₁₂	C₂×C₃²	1	1	yes	characteristic, complemented
116	C₃×AGL(1,ℤ/8)	—	3	32	no	—
117	C₂×C₃×SD₁₆	—	3	8	no	—
118	C₂×C₃×D₈	—	3	8	no	—
119	C₂×C₃×M₁₆	—	3	4	no	—
120	#949	C₂×C₃²	1	8	yes	direct product factor
121	C₂×#215	C₂×C₃²	1	2	yes	complemented
122	C₂×#213	C₂×C₃²	1	2	yes	complemented
123	C₂×#208	C₂×C₃²	1	1	yes	characteristic, complemented
124	C₂³×C₃²	—	2	8	no	—
125	C₂³×C₃²	—	2	1	no	—
126	C₂³×C₃²	—	2	4	no	—
127	C₂³×C₃²	—	2	4	no	—
128	C₂³×C₃²	—	6	4	no	—
129	C₂³×C₃²	—	6	2	no	—
130	C₂³×C₃²	—	12	4	no	—
131	C₂³×C₃²	#67	1	1	yes	characteristic
132	C₂³×C₃²	C₃×D₄	1	4	yes	—
133	C₂²×C₃×D₃	—	2	8	no	—
134	C₂²×C₃×D₃	—	2	16	no	—
135	C₂²×C₃×D₃	—	4	16	no	—
136	C₃²×Q₈	—	2	8	no	—
137	C₃²×Q₈	—	2	1	no	—
138	C₃²×Q₈	—	2	4	no	—
139	C₃²×Q₈	—	2	8	no	—
140	C₃²×Q₈	C₂²×D₃	1	2	yes	complemented
141	C₃²×Q₈	C₂³×C₃	1	8	yes	complemented
142	C₃²×D₄	—	2	32	no	—
143	C₃²×D₄	—	2	8	no	—
144	C₃²×D₄	—	2	4	no	—
145	C₃²×D₄	—	2	16	no	—
146	C₃²×D₄	—	2	1	no	—
147	C₃²×D₄	—	2	4	no	—
148	C₃²×D₄	—	2	8	no	—
149	C₃²×D₄	—	3	4	no	—
150	C₃²×D₄	—	6	4	no	—
151	C₃²×D₄	—	6	2	no	—
152	C₃²×D₄	C₂²×D₃	1	2	yes	complemented
153	C₃²×D₄	C₂³×C₃	1	8	yes	complemented
154	C₂×C₃²×C₄	—	2	8	no	—
155	C₂×C₃²×C₄	—	2	32	no	—
156	C₂×C₃²×C₄	—	2	1	no	—
157	C₂×C₃²×C₄	—	2	4	no	—
158	C₂×C₃²×C₄	—	2	4	no	—
159	C₂×C₃²×C₄	—	2	16	no	—
160	C₂×C₃²×C₄	—	2	4	no	—
161	C₂×C₃²×C₄	—	2	8	no	—
162	C₂×C₃²×C₄	—	2	4	no	—
163	C₂×C₃²×C₄	—	2	8	no	—
164	C₂×C₃²×C₄	#67	1	2	yes	—
165	C₂×C₃²×C₄	#67	1	1	yes	characteristic
166	C₂×C₃²×C₄	C₃×D₄	1	4	yes	—
167	C₂×C₃²×C₄	C₃×D₄	1	8	yes	—
168	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	—
169	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
170	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
171	C₂×C₃²×C₄	C₂³×C₃	1	8	yes	—
172	C₃×D₁₂	—	2	8	no	—
173	C₃×D₁₂	—	2	16	no	—
174	C₃×D₁₂	C₂³×C₃	1	16	yes	—
175	C₃²×C₈	—	3	4	no	—
176	C₃×C₃⋊C₈	C₂³×C₃	1	16	yes	complemented
177	C₂×AGL(1,ℤ/8)	—	3	1	no	Sylow
178	C₂×C₃³	—	2	2	no	—
179	C₂×C₃³	—	4	2	no	—
180	C₂×C₃³	AGL(1,ℤ/8)	1	2	yes	complemented
181	C₂×C₃³	C₂²×D₄	1	1	yes	characteristic
182	C₃²×D₃	—	4	4	no	—
183	C₂⁴×C₃	—	6	4	no	—
184	C₂³×D₃	—	2	1	no	—
185	C₃×#41	—	2	16	no	—
186	C₃×#41	—	2	8	no	—
187	C₃×#41	—	2	2	no	—
188	C₃×#41	—	2	16	no	—
189	C₃×#41	C₂×C₃×D₃	1	16	yes	complemented
190	C₃×#41	C₂²×C₃²	1	4	yes	complemented
191	C₂×C₃×Q₈	—	2	4	no	—
192	C₂×C₃×Q₈	C₂×C₃×D₃	1	4	yes	complemented
193	C₂×C₃×Q₈	C₂²×C₃²	1	1	yes	characteristic, complemented
194	C₂×C₃×D₄	—	2	8	no	—
195	C₂×C₃×D₄	—	2	4	no	—
196	C₂×C₃×D₄	—	2	1	no	—
197	C₂×C₃×D₄	—	2	4	no	—
198	C₂×C₃×D₄	—	3	8	no	—
199	C₂×C₃×D₄	—	3	16	no	—
200	C₂×C₃×D₄	—	6	4	no	—
201	C₂×C₃×D₄	—	6	8	no	—
202	C₂×C₃×D₄	C₂×C₃×D₃	1	4	yes	complemented
203	C₂×C₃×D₄	C₂²×C₃²	1	1	yes	characteristic, complemented
204	C₂²×C₃×C₄	—	2	8	no	—
205	C₂²×C₃×C₄	—	2	4	no	—
206	C₂²×C₃×C₄	—	2	1	no	—
207	C₂²×C₃×C₄	—	2	4	no	—
208	C₂²×C₃×C₄	C₂×C₃×D₃	1	4	yes	—
209	C₂²×C₃×C₄	C₂²×C₃²	1	1	yes	characteristic
210	C₂×D₁₂	—	2	2	no	—
211	C₂×D₁₂	—	2	1	no	—
212	C₂×D₁₂	C₂²×C₃²	1	2	yes	—
213	C₂×D₁₂	C₂²×C₃²	1	4	yes	complemented
214	C₃×SD₁₆	—	3	32	no	—
215	C₃×D₈	—	3	32	no	—
216	C₃×M₁₆	—	3	16	no	—
217	C₂×C₃×C₈	—	3	8	no	—
218	#215	C₂²×C₃²	1	8	yes	complemented
219	#213	C₂²×C₃²	1	8	yes	complemented
220	#208	C₂²×C₃²	1	4	yes	complemented
221	C₂×C₃⋊C₈	C₂²×C₃²	1	2	yes	complemented
222	C₂²×C₃²	—	2	2	no	—
223	C₂²×C₃²	—	2	16	no	—
224	C₂²×C₃²	—	2	2	no	—
225	C₂²×C₃²	—	2	8	no	—
226	C₂²×C₃²	—	2	4	no	—
227	C₂²×C₃²	—	2	8	no	—
228	C₂²×C₃²	—	2	8	no	—
229	C₂²×C₃²	—	4	8	no	—
230	C₂²×C₃²	—	4	16	no	—
231	C₂²×C₃²	—	4	2	no	—
232	C₂²×C₃²	—	4	8	no	—
233	C₂²×C₃²	—	6	4	no	—
234	C₂²×C₃²	—	12	8	no	—
235	C₂²×C₃²	—	12	4	no	—
236	C₂²×C₃²	C₂×#67	1	2	yes	—
237	C₂²×C₃²	C₂×#67	1	1	yes	characteristic
238	C₂²×C₃²	C₂×C₃×D₄	1	8	yes	—
239	C₂²×C₃²	C₂×C₃×D₄	1	4	yes	—
240	C₂×C₃×D₃	—	2	16	no	—
241	C₂×C₃×D₃	—	4	32	no	—
242	C₂×C₃×D₃	—	4	16	no	—
243	C₃²×C₄	—	2	16	no	—
244	C₃²×C₄	—	2	2	no	—
245	C₃²×C₄	—	2	8	no	—
246	C₃²×C₄	—	2	4	no	—
247	C₃²×C₄	—	2	8	no	—
248	C₃²×C₄	—	2	4	no	—
249	C₃²×C₄	C₂×#67	1	2	yes	—
250	C₃²×C₄	C₂×#67	1	1	yes	characteristic
251	C₃²×C₄	C₂×C₃×D₄	1	8	yes	—
252	C₃²×C₄	C₂×C₃×D₄	1	4	yes	—
253	C₃²×C₄	C₂³×D₃	1	1	yes	characteristic
254	C₃²×C₄	C₂⁴×C₃	1	4	yes	—
255	C₂×#41	C₃²×D₃	1	1	yes	characteristic, complemented
256	C₂²×D₄	—	3	1	no	—
257	AGL(1,ℤ/8)	—	3	8	no	—
258	C₂×SD₁₆	—	3	2	no	—
259	C₂×D₈	—	3	2	no	—
260	C₂×M₁₆	—	3	1	no	—
261	C₃³	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic, complemented, Sylow
262	C₂³×C₃	—	2	8	no	—
263	C₂³×C₃	—	2	4	no	—
264	C₂³×C₃	—	2	1	no	—
265	C₂³×C₃	—	2	4	no	—
266	C₂³×C₃	—	6	16	no	—
267	C₂³×C₃	—	6	8	no	—
268	C₂³×C₃	—	12	16	no	—
269	C₂³×C₃	C₃×#67	1	4	yes	—
270	C₂³×C₃	C₃²×D₄	1	1	yes	characteristic
271	C₂²×D₃	—	2	2	no	—
272	C₂²×D₃	—	2	4	no	—
273	C₂²×D₃	—	4	4	no	—
274	C₃×Q₈	—	2	8	no	—
275	C₃×Q₈	—	2	4	no	—
276	C₃×Q₈	—	2	1	no	—
277	C₃×Q₈	—	2	8	no	—
278	C₃×Q₈	C₂²×C₃×D₃	1	8	yes	complemented
279	C₃×Q₈	C₂³×C₃²	1	2	yes	complemented
280	C₃×D₄	—	2	32	no	—
281	C₃×D₄	—	2	8	no	—
282	C₃×D₄	—	2	16	no	—
283	C₃×D₄	—	2	4	no	—
284	C₃×D₄	—	2	4	no	—
285	C₃×D₄	—	2	1	no	—
286	C₃×D₄	—	2	8	no	—
287	C₃×D₄	—	3	16	no	—
288	C₃×D₄	—	6	16	no	—
289	C₃×D₄	—	6	8	no	—
290	C₃×D₄	C₂²×C₃×D₃	1	8	yes	complemented
291	C₃×D₄	C₂³×C₃²	1	2	yes	complemented
292	C₂×C₃×C₄	—	2	8	no	—
293	C₂×C₃×C₄	—	2	32	no	—
294	C₂×C₃×C₄	—	2	4	no	—
295	C₂×C₃×C₄	—	2	1	no	—
296	C₂×C₃×C₄	—	2	16	no	—
297	C₂×C₃×C₄	—	2	4	no	—
298	C₂×C₃×C₄	—	2	4	no	—
299	C₂×C₃×C₄	—	2	8	no	—
300	C₂×C₃×C₄	—	2	4	no	—
301	C₂×C₃×C₄	—	2	8	no	—
302	C₂×C₃×C₄	C₃×#67	1	4	yes	—
303	C₂×C₃×C₄	C₃×#67	1	8	yes	—
304	C₂×C₃×C₄	C₃²×D₄	1	1	yes	characteristic
305	C₂×C₃×C₄	C₃²×D₄	1	2	yes	—
306	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
307	C₂×C₃×C₄	C₂²×C₃×D₃	1	8	yes	—
308	C₂×C₃×C₄	C₂³×C₃²	1	1	yes	characteristic
309	C₂×C₃×C₄	C₂³×C₃²	1	2	yes	—
310	D₁₂	—	2	2	no	—
311	D₁₂	—	2	4	no	—
312	D₁₂	C₂³×C₃²	1	4	yes	—
313	C₃×C₈	—	3	16	no	—
314	C₃⋊C₈	C₂³×C₃²	1	4	yes	complemented
315	C₂×C₃²	—	2	2	no	—
316	C₂×C₃²	—	2	8	no	—
317	C₂×C₃²	—	2	4	no	—
318	C₂×C₃²	—	2	8	no	—
319	C₂×C₃²	—	4	8	no	—
320	C₂×C₃²	—	4	16	no	—
321	C₂×C₃²	—	4	8	no	—
322	C₂×C₃²	—	4	2	no	—
323	C₂×C₃²	—	12	4	no	—
324	C₂×C₃²	#949	1	2	yes	direct product factor
325	C₂×C₃²	C₃×AGL(1,ℤ/8)	1	8	yes	complemented
326	C₂×C₃²	C₂²×#67	1	1	yes	characteristic
327	C₂×C₃²	C₂²×C₃×D₄	1	4	yes	—
328	C₃×D₃	—	4	16	no	—
329	C₂⁴	—	6	1	no	—
330	#41	—	2	2	no	—
331	#41	C₂×C₃²×D₃	1	4	yes	complemented
332	C₂×Q₈	C₂×C₃²×D₃	1	1	yes	characteristic, complemented
333	C₂×D₄	—	2	1	no	—
334	C₂×D₄	—	3	2	no	—
335	C₂×D₄	—	3	4	no	—
336	C₂×D₄	—	6	1	no	—
337	C₂×D₄	—	6	2	no	—
338	C₂×D₄	C₂×C₃²×D₃	1	1	yes	characteristic, complemented
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	C₂×C₃²×D₃	1	1	yes	characteristic
341	SD₁₆	—	3	8	no	—
342	D₈	—	3	8	no	—
343	M₁₆	—	3	4	no	—
344	C₂×C₈	—	3	2	no	—
345	C₂²×C₃	—	2	8	no	—
346	C₂²×C₃	—	2	2	no	—
347	C₂²×C₃	—	2	16	no	—
348	C₂²×C₃	—	2	8	no	—
349	C₂²×C₃	—	2	2	no	—
350	C₂²×C₃	—	2	4	no	—
351	C₂²×C₃	—	2	8	no	—
352	C₂²×C₃	—	4	8	no	—
353	C₂²×C₃	—	4	16	no	—
354	C₂²×C₃	—	4	8	no	—
355	C₂²×C₃	—	4	2	no	—
356	C₂²×C₃	—	6	16	no	—
357	C₂²×C₃	—	12	32	no	—
358	C₂²×C₃	—	12	16	no	—
359	C₂²×C₃	C₂×C₃×#67	1	8	yes	—
360	C₂²×C₃	C₂×C₃×#67	1	4	yes	—
361	C₂²×C₃	C₂×C₃²×D₄	1	2	yes	—
362	C₂²×C₃	C₂×C₃²×D₄	1	1	yes	characteristic
363	C₂×D₃	—	2	4	no	—
364	C₂×D₃	—	4	8	no	—
365	C₂×D₃	—	4	4	no	—
366	C₃×C₄	—	2	16	no	—
367	C₃×C₄	—	2	8	no	—
368	C₃×C₄	—	2	2	no	—
369	C₃×C₄	—	2	4	no	—
370	C₃×C₄	—	2	8	no	—
371	C₃×C₄	—	2	4	no	—
372	C₃×C₄	C₂×C₃×#67	1	8	yes	—
373	C₃×C₄	C₂×C₃×#67	1	4	yes	—
374	C₃×C₄	C₂×C₃²×D₄	1	2	yes	—
375	C₃×C₄	C₂×C₃²×D₄	1	1	yes	characteristic
376	C₃×C₄	C₂³×C₃×D₃	1	4	yes	—
377	C₃×C₄	C₂⁴×C₃²	1	1	yes	characteristic
378	C₃²	—	2	4	no	—
379	C₃²	C₂×#949	1	1	yes	characteristic, direct product factor
380	C₃²	C₂×C₃×AGL(1,ℤ/8)	1	4	yes	complemented
381	C₂³	—	2	1	no	—
382	C₂³	—	6	4	no	—
383	C₂³	—	6	2	no	—
384	C₂³	—	12	4	no	—
385	C₂³	C₃²×#67	1	1	yes	characteristic
386	Q₈	—	2	1	no	—
387	Q₈	C₂²×C₃²×D₃	1	2	yes	complemented
388	D₄	—	2	4	no	—
389	D₄	—	2	1	no	—
390	D₄	—	3	4	no	—
391	D₄	—	6	4	no	—
392	D₄	—	6	2	no	—
393	D₄	C₂²×C₃²×D₃	1	2	yes	complemented
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	4	no	—
396	C₂×C₄	C₃²×#67	1	1	yes	characteristic
397	C₂×C₄	C₃²×#67	1	2	yes	—
398	C₂×C₄	C₂²×C₃²×D₃	1	1	yes	characteristic
399	C₂×C₄	C₂²×C₃²×D₃	1	2	yes	—
400	C₈	—	3	4	no	—
401	C₂×C₃	—	2	2	no	—
402	C₂×C₃	—	2	8	no	—
403	C₂×C₃	—	2	8	no	—
404	C₂×C₃	—	2	4	no	—
405	C₂×C₃	—	4	8	no	—
406	C₂×C₃	—	4	16	no	—
407	C₂×C₃	—	4	2	no	—
408	C₂×C₃	—	4	8	no	—
409	C₂×C₃	—	12	16	no	—
410	C₂×C₃	C₃×#949	1	8	yes	direct product factor
411	C₂×C₃	C₃²×AGL(1,ℤ/8)	1	2	yes	complemented
412	C₂×C₃	C₂²×C₃×#67	1	4	yes	—
413	C₂×C₃	C₂²×C₃²×D₄	1	1	yes	characteristic
414	D₃	—	4	4	no	—
415	C₂²	—	2	2	no	—
416	C₂²	—	2	2	no	—
417	C₂²	—	4	2	no	—
418	C₂²	—	6	4	no	—
419	C₂²	—	12	8	no	—
420	C₂²	—	12	4	no	—
421	C₂²	C₂×C₃²×#67	1	2	yes	—
422	C₂²	C₂×C₃²×#67	1	1	yes	characteristic
423	C₄	—	2	2	no	—
424	C₄	C₂×C₃²×#67	1	2	yes	—
425	C₄	C₂×C₃²×#67	1	1	yes	characteristic
426	C₄	C₂³×C₃²×D₃	1	1	yes	characteristic
427	C₃	—	2	4	no	—
428	C₃	C₂×C₃×#949	1	4	yes	direct product factor
429	C₃	C₂×C₃²×AGL(1,ℤ/8)	1	1	yes	characteristic, complemented
430	C₂	—	2	2	no	—
431	C₂	—	4	2	no	—
432	C₂	—	12	4	no	—
433	C₂	C₃²×#949	1	2	yes	direct product factor
434	C₂	C₂²×C₃²×#67	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃²	C₂×#67
commutator, cosocle	C₃×C₄	C₂⁴×C₃²
Frattini	C₄	C₂³×C₃²×D₃
Fitting	C₂×C₃³×#41	C₂
socle	C₂²×C₃³	C₂×D₄
hypercenter	C₂×C₃²×#41	D₃
hypocenter	C₃	C₂×C₃²×AGL(1,ℤ/8)
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃² ◁ C₂²×C₃²×C₄ ◁ C₂×C₃²×#41

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×C₃³×#41	C₂	semidirect
2. C₂²×C₃²×D₁₂	C₂	semidirect
3. C₃²×#949	C₂	direct (N × H)
4. C₂×C₃²×#215	C₂	semidirect
5. C₂×C₃²×#213	C₂	semidirect
6. C₂×C₃²×#208	C₂	semidirect
8. C₂×C₃×#949	C₃	direct (N × H)
11. C₃³×#41	C₂²	semidirect
12. C₂×C₃³×Q₈	C₂²	semidirect
14. C₂×C₃³×D₄	C₂²	semidirect
20. C₂×C₃²×D₁₂	C₂²	semidirect
21. C₃²×#215	C₂²	semidirect
22. C₃²×#213	C₂²	semidirect
23. C₃²×#208	C₂²	semidirect
24. C₂×C₃²×C₃⋊C₈	C₂²	semidirect
26. C₂×C₃²×#41	D₃	semidirect
27. C₂×C₃²×#41	C₂×C₃	semidirect
29. C₂²×C₃×D₁₂	C₂×C₃	semidirect
34. C₃×#949	C₂×C₃	direct (N × H)
35. C₂×C₃×#215	C₂×C₃	semidirect
36. C₂×C₃×#213	C₂×C₃	semidirect
37. C₂×C₃×#208	C₂×C₃	semidirect
44. C₃³×Q₈	C₂³	semidirect
47. C₃³×D₄	C₂³	semidirect
57. C₃²×C₃⋊C₈	C₂³	semidirect
59. C₂×#949	C₃²	direct (N × H)
66. C₃²×#41	C₂×D₃	semidirect
67. C₃²×#41	C₂²×C₃	semidirect
69. C₂×C₃²×Q₈	C₂×D₃	semidirect
70. C₂×C₃²×Q₈	C₂²×C₃	semidirect
79. C₂×C₃²×D₄	C₂×D₃	semidirect
80. C₂×C₃²×D₄	C₂²×C₃	semidirect
90. C₂×C₃×D₁₂	C₂²×C₃	semidirect
95. C₃×#215	C₂²×C₃	semidirect
96. C₃×#213	C₂²×C₃	semidirect
97. C₃×#208	C₂²×C₃	semidirect
98. C₂×C₃×C₃⋊C₈	C₂²×C₃	semidirect
112. C₂×C₃×#41	C₃×D₃	semidirect
113. C₂×C₃×#41	C₂×C₃²	semidirect
115. C₂²×D₁₂	C₂×C₃²	semidirect
120. #949	C₂×C₃²	direct (N × H)
121. C₂×#215	C₂×C₃²	semidirect
122. C₂×#213	C₂×C₃²	semidirect
123. C₂×#208	C₂×C₃²	semidirect
140. C₃²×Q₈	C₂²×D₃	semidirect
141. C₃²×Q₈	C₂³×C₃	semidirect
152. C₃²×D₄	C₂²×D₃	semidirect
153. C₃²×D₄	C₂³×C₃	semidirect
176. C₃×C₃⋊C₈	C₂³×C₃	semidirect
180. C₂×C₃³	AGL(1,ℤ/8)	semidirect
189. C₃×#41	C₂×C₃×D₃	semidirect
190. C₃×#41	C₂²×C₃²	semidirect
192. C₂×C₃×Q₈	C₂×C₃×D₃	semidirect
193. C₂×C₃×Q₈	C₂²×C₃²	semidirect
202. C₂×C₃×D₄	C₂×C₃×D₃	semidirect
203. C₂×C₃×D₄	C₂²×C₃²	semidirect
213. C₂×D₁₂	C₂²×C₃²	semidirect
218. #215	C₂²×C₃²	semidirect
219. #213	C₂²×C₃²	semidirect
220. #208	C₂²×C₃²	semidirect
221. C₂×C₃⋊C₈	C₂²×C₃²	semidirect
255. C₂×#41	C₃²×D₃	semidirect
261. C₃³	C₂×AGL(1,ℤ/8)	semidirect
278. C₃×Q₈	C₂²×C₃×D₃	semidirect
279. C₃×Q₈	C₂³×C₃²	semidirect
290. C₃×D₄	C₂²×C₃×D₃	semidirect
291. C₃×D₄	C₂³×C₃²	semidirect
314. C₃⋊C₈	C₂³×C₃²	semidirect
324. C₂×C₃²	#949	direct (N × H)
325. C₂×C₃²	C₃×AGL(1,ℤ/8)	semidirect
331. #41	C₂×C₃²×D₃	semidirect
332. C₂×Q₈	C₂×C₃²×D₃	semidirect
338. C₂×D₄	C₂×C₃²×D₃	semidirect
379. C₃²	C₂×#949	direct (N × H)
380. C₃²	C₂×C₃×AGL(1,ℤ/8)	semidirect
387. Q₈	C₂²×C₃²×D₃	semidirect
393. D₄	C₂²×C₃²×D₃	semidirect
410. C₂×C₃	C₃×#949	direct (N × H)
411. C₂×C₃	C₃²×AGL(1,ℤ/8)	semidirect
428. C₃	C₂×C₃×#949	direct (N × H)
429. C₃	C₂×C₃²×AGL(1,ℤ/8)	semidirect
433. C₂	C₃²×#949	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₃³×#41	2
C₂²×C₃²×D₁₂	2
C₃²×#949	2
C₂×C₃²×#215	2
C₂×C₃²×#213	2
C₂×C₃²×#208	2
C₂×C₃²×AGL(1,ℤ/8)	3
C₂×C₃×#949	3

Subgroups — C2×C32×#949 #13179200

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃²×#949 #13179200